Question

exponential functions

1. jane decided to purchase one lottery ticket. against all odds, she won! she decided to buy

er dream car, a tesla, for $45,000. the value of her car will depreciate at 12% per year; but
she won so much money she doesn’t care about that. write an equation, v(t) = to represent the
value of jane’s car. (hint: is percent decrease exponential or linear?)

Explanation:

Step1: Identify the type of depreciation

Since the car's value depreciates by a percentage (12% per year), it's exponential depreciation. The general formula for exponential depreciation is \( V(t)=V_0(1 - r)^t \), where \( V_0 \) is the initial value, \( r \) is the rate of depreciation, and \( t \) is time in years.

Step2: Determine the values of \( V_0 \) and \( r \)

The initial value of the car \( V_0 = 45000 \) dollars. The depreciation rate \( r = 12\%=0.12 \).

Step3: Substitute the values into the formula

Substitute \( V_0 = 45000 \) and \( r = 0.12 \) into the exponential depreciation formula. So \( 1 - r=1 - 0.12 = 0.88 \). Then the equation for the value of the car as a function of time \( t \) is \( V(t)=45000(0.88)^t \).

Answer:

\( V(t) = 45000(0.88)^t \)